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Estimation of Data Measured with Error and Subject to Linear Restrictions

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  • Weale, Martin

Abstract

Variables are often measured subject to error, whether they are collected as part of an experiment or by sample surveys. A consequence of this is that there will be different estimates of the same variable, or, more generally, linear restrictions which the observations should satisfy but fail to. With knowledge of the variances of the various observations, it has been shown elsewhere that maximum-likelihood estimates of the observations can be produced. This paper shows how, given a sequence of such observations, estimates can be produced without knowledge of data reliabilities. The method is applied to estimates of constant price U.S. GNP. It suggests that 64 per cent of the discrepancy should be attributed to the expenditure estimate, with only 36 per cent going to the income/output estimate. The current method of presentation, on the other hand, places the whole of the error in the income/output estimate. Copyright 1992 by John Wiley & Sons, Ltd.

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  • Weale, Martin, 1992. "Estimation of Data Measured with Error and Subject to Linear Restrictions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(2), pages 167-174, April-Jun.
    • Handle: RePEc:jae:japmet:v:7:y:1992:i:2:p:167-74
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    Cited by:

    1. Ryan Greenaway-McGrevy, 2011. "Is GDP or GDI a better measure of output? A statistical approach," BEA Working Papers 0076, Bureau of Economic Analysis.
    2. Martín Almuzara & Gabriele Fiorentini & Enrique Sentana, 2023. "Aggregate Output Measurements: A Common Trend Approach," Advances in Econometrics, in: Essays in Honor of Joon Y. Park: Econometric Methodology in Empirical Applications, volume 45, pages 3-33, Emerald Group Publishing Limited.
    3. Christopher Bajada, 2001. "An Examination of the Statistical Discrepancy and Private Investment Expenditure," Journal of Applied Economics, Universidad del CEMA, vol. 4, pages 27-61, May.
    4. Jan P. A. M. Jacobs & Samad Sarferaz & Jan-Egbert Sturm & Simon van Norden, 2022. "Can GDP Measurement Be Further Improved? Data Revision and Reconciliation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(1), pages 423-431, January.
    5. Dennis J. Fixler & Jeremy J. Nalewaik, 2007. "News, noise, and estimates of the \"true\" unobserved state of the economy," Finance and Economics Discussion Series 2007-34, Board of Governors of the Federal Reserve System (U.S.).
    6. Martín Almuzara & Dante Amengual & Gabriele Fiorentini & Enrique Sentana, 2024. "GDP Solera: The Ideal Vintage Mix," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 42(3), pages 984-997, July.
    7. Athanasopoulos, George & Hyndman, Rob J. & Kourentzes, Nikolaos & Panagiotelis, Anastasios, 2024. "Forecast reconciliation: A review," International Journal of Forecasting, Elsevier, vol. 40(2), pages 430-456.
    8. Eiji Goto & Jan P.A.M. Jacobs & Tara M. Sinclair & Simon van Norden, 2023. "Employment reconciliation and nowcasting," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(7), pages 1007-1017, November.
    9. Víctor Guerrero & Fabio Nieto, 1999. "Temporal and contemporaneous disaggregation of multiple economic time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 8(2), pages 459-489, December.

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